It is common to define egalitarianism in terms of an inequality ordering, which is supposed to have some weight in overall evaluations of outcomes. Egalitarianism, thus defined, implies that levelling down makes the outcome better in respect of reducing inequality; however, the levelling down objection claims there can be nothing good about levelling down. The priority view, on the other hand, does not have this implication. This paper challenges the common view. The standard definition of egalitarianism implicitly assumes a context. Once this context is made clear, it is easily seen that egalitarianism could be defined alternatively in terms of valuing a benefit to a person inversely to how well off he is relative to others. The levelling down objection does not follow from this definition. Moreover, the common definition does not separate egalitarian orderings from prioritarian ones. It is useful to do this by requiring that on egalitarianism, additively separable orderings should be excluded. But this requirement is stated as a condition on the alternative definition of egalitarianism, from which the levelling down objection does not follow.